270003 maks2 mainms - emaths papers/ks2 sat papers/ks2 mathematics... · recording marks awarded on...

Mathematics tests

Mark schemes

Test A, test B and mental mathematics test

MaKEY STAGE

2LEVELS

3–52006

2006

First published in 2006

© Qualifi cations and Curriculum Authority 2006

Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is

prohibited without prior written permission of the publisher, unless within the terms of licences issued by

the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study,

criticism or review, or by educational institutions solely for educational purposes, without permission,

provided full acknowledgement is given.

Produced in Great Britain by the Qualifi cations and Curriculum Authority under the authority and

superintendence of the Controller of Her Majesty’s Stationery Offi ce and Queen’s Printer of Acts

of Parliament.

The Qualifi cations and Curriculum Authority is an exempt charity under Schedule 2 of the Charities

Act 1993.

Qualifi cations and Curriculum Authority

83 Piccadilly

London W1J 8QA

www.qca.org.uk

1

Marking the mathematics tests

As in 2005, external markers, employed by the external marking agencies under

contract to QCA, will mark the test papers. The markers will follow the mark schemes

in this booklet, which is supplied to teachers for information.

This booklet contains the mark schemes for the levels 3–5 tests A, B and mental

mathematics. Level threshold tables will be available on the QCA website on

19 June 2006 (www.qca.org.uk).

General guidance

The structure of the mark schemes

The marking information for each question is set out in the form of tables, which start

on page 6 of this booklet. The ‘question’ column on the left-hand side of each table

provides a quick reference to the question number and the question part. The ‘mark’

column indicates the total number of marks available for each question part. On some

occasions the symbol U1 may be shown in the mark column. The ‘U’ indicates that

there is a Using and applying mathematics element in the question. The number, 1,

shows the number of marks attributed to using and applying mathematics in

this question.

The ‘requirement’ column may include two types of information:

a statement of the requirements for the award of each mark, with an indication of

whether credit can be given for correct working

examples of some different types of correct response.

The ‘additional guidance’ column indicates alternative acceptable responses, and

provides details of specifi c types of response which are unacceptable. Other guidance,

such as the range of acceptable answers, is provided as necessary.

Additionally, for the mental mathematics test, general guidance on marking is given on

page 18, together with a ‘quick reference’ mark scheme.

Applying the mark schemes

In order to ensure consistency of marking, the most frequent procedural queries are

listed on pages 2 and 3 with the action the marker will take. This is followed by further

guidance on pages 4 and 5 relating to the marking of questions that involve money,

time and other measures. Unless otherwise specifi ed in the mark scheme, markers will

apply the following guidelines in all cases.

2

What if ... Marking procedure

The pupil’s response is

numerically or algebraically

equivalent to the answer

in the mark scheme.

Markers will award the mark unless the mark scheme states otherwise.

The pupil’s response does

not match closely any of the

examples given.

Markers will use their judgement in deciding whether the response corresponds with

the statement of the requirements given in the ‘requirement’ column. Reference will

also be made to the additional guidance and, if there is still uncertainty, markers will

contact the supervising marker.

The pupil has responded

in a non-standard way.

Calculations, formulae and written responses do not have to be set out in any

particular format. Pupils may provide evidence in any form as long as its meaning

can be understood. Diagrams, symbols or words are acceptable for explanations or

for indicating a response. Any correct method of setting out working, however

idiosyncratic, will be accepted.

There appears to be a

misreading affecting

the working.

This is when the pupil misreads the information given in the question and uses

different information without altering the original intention or diffi culty level of the

question. For each misread that occurs, one mark only will be deducted.

In one-mark questions – 0 marks are awarded.

In two-mark questions that have a method mark – 1 mark will be awarded if the

correct method is correctly implemented with the misread number.

No answer is given in

the expected place, but

the correct answer is

given elsewhere.

Where a pupil has shown understanding of the question, the mark(s) will be given.

In particular, where a word or number response is expected, a pupil may meet the

requirement by annotating a graph or labelling a diagram elsewhere in the question.

The response in the answer

box is wrong, but

the correct answer is shown

in the working.

Where appropriate, detailed guidance will

be given in the mark scheme, which markers

will follow. If no guidance is given, markers

will examine each case to decide whether:

the incorrect answer is due to a

transcription error

the pupil has continued to give redundant

extra working which does not contradict

work already done

the pupil has continued to give redundant

extra working which does contradict work

already done.

If so, the mark will be awarded.

If so, the mark will be awarded.

If so, the mark will not be awarded.

3

What if ... Marking procedure

The pupil’s answer is

correct but the wrong

working is shown.

A correct response will always be marked as correct.

The correct response has

been crossed out and

not replaced.

Any legible crossed-out work that has not been replaced will be marked

according to the mark scheme. If the work is replaced, then crossed-out work

will not be considered.

More than one answer

is given.

If all answers are correct (or a range of answers is given, all of which are

correct), the mark will be awarded unless prohibited by the mark scheme.

If both correct and incorrect responses are given, no mark will be awarded.

The answer is correct

but, in a later part of the

question, the pupil has

contradicted this response.

A mark given for one part will not be disallowed for working or answers given

in a different part, unless the mark scheme specifi cally states otherwise.

The pupil has drawn lines

which do not meet at the

correct point.

Markers will interpret the phrase ‘slight inaccuracies in drawing’ to mean

‘within or on a circle of radius 2mm with centre at the correct point’.

within the circleaccepted

on the circleaccepted

outside the circlenot accepted

Recording marks awarded on the test paper

All questions, even those not attempted by the pupil, will be marked with a ‘1’ or ‘0’

entered in each marking space.

A two-mark question which is correct will have ‘1’ entered in both marking spaces.

A two-mark question which is incorrect, but which has suffi cient evidence of working

or method as required by the mark scheme, will have ‘1’ entered in the fi rst marking

space and ‘0’ in the second. Otherwise ‘0’ will be entered in both marking spaces.

For the written tests, the total number of marks gained on each double page will be

written in the space at the bottom of the right-hand page. For all of the tests, the total

number of marks gained on each paper will be recorded on the front of the test paper,

and on the mark sheet.

Test A carries a total of 40 marks. Test B also carries a total of 40 marks. The mental

mathematics test carries a total of 20 marks.

The 2006 key stage 2 mathematics tests and mark schemes were developed by the

Mathematics Test Development Team at Edexcel.

4

Marking specifi c types of question – summary of additionalguidance

Responses involving money

Question Accept Do not accept

Where the £ sign is given

for example:

£3.20, £7

£

£3.20 £7

£7.00

Any unambiguous indication of the correct amount, eg

£3.20p

£3 20 pence

£3 20

£3,20

£3-20

£3:20

Incorrect placement of pounds or pence, eg

£320

£320p

Incorrect placement of decimal point,or incorrect use or omission of 0, eg

£3.2

£3 200

£32 0

£3-2-0

Where the p sign is given

for example:

40p

p

40p


£0.40p

Incorrect or ambiguous use of pounds or pence, eg

0.40p

£40p

Where nosign is given

for example:

£3.20, 40p

£3.20 40p

320p £0.40


£3.20p £0.40p

£3 20 pence £.40p

£3 20 £.40

£3,20 40

£3-20 0.40

£3:20

3.20

320

3 pounds 20

Incorrect or ambiguous use of pounds or pence, eg

£320 £40

£320p £40p

£3.2 0.4

3.20p

5

Responses involving time


A timeinterval

for example:

2 hours 30minutes

2 hours 30 minutes

Any unambiguous, correct indication, eg

212 hours

2.5 hours

2h 30

2h 30min

150 minutes

150

Digital electronic time, ie

2:30

Incorrect or ambiguous time interval, eg

2.30

2-30

2,30

2.3

2.3 hours

2.3h

2h 3

2.30 min

A specifi ctime

for example:

8:40am, 17:20

8:40am

8:40

twenty to nine

Any unambiguous, correct indication, eg

08.40

8.40

0840

8 40

8-40

8,40

Unambiguous change to 12 or 24 hour clock, eg

17:20 as 5:20pm or 17:20pm

Incorrect time, eg

8.4am

8.40pm

Incorrect placement of separators, spaces etc or incorrect use or omission of 0, eg

840

8:4:0

8.4

084

84

Responses involving measures


Where unitsare given(eg kg, m, l)

for example:

8.6kg

kg

8.6kg

Any unambiguous indication of the correct measurement, eg

8.60kg

8.6000kg

8kg 600g

Incorrect or ambiguous use of units, eg

8600kg

Note

If a pupil leaves the answer box empty but writes the answer elsewhere on the page,

then that answer must be consistent with the units given in the answer box and the

conditions listed above.

If a pupil changes the unit given in the answer box, then their answer must be

equivalent to the correct answer using the unit they have chosen, unless otherwise

indicated in the mark scheme.

6

Test A questions 1–3

Question Requirement Mark Additional guidance

1 Numbers written in correct order as shown:

109 190 901 910 1091

1m

2 One line of symmetry correctly positioned on each diagram as shown:

1m Accept slight inaccuracies in drawing provided the intention is clear.

The length of the line is unimportant provided the intention is clear.

3a

3b

Graph completed as shown:

0

2

4

6

Numberof birds

8

Blackbird Sparrow Robin Blue tit Other

14

1m

1m

Accept bar for ‘blue tit’ in the range 2.5 to 3.5 exclusive.

Accept bar for ‘other’ within 2mm of correct length.

Accept equivalent fractions, eg 520

Do not accept 5

7



4a

4b

4

150

1m

1m

5 Diagram completed as shown:

30 70

20

1m

6a

6b

1 hour 20 minutes

3:25

1m

1m

The answer is a time interval(see page 5 for guidance).

The answer is a specifi c time(see page 5 for guidance).

7a

7b

Boxes ticked as shown:

Boxes ticked as shown:

1m

U1

1m

U1

Accept alternative unambiguous indications such as Y or N.

Accept alternative unambiguous indications such as Y or N.

8a

8b

451

110

1m

1m

8



9 Award TWO marks for the correct answer of 5

If the answer is incorrect, award ONEmark for evidence of appropriate working, eg

5 × 25 = 125

12 × 10 = 120

125 – 120 = wrong answer

Up to2m

Calculation must be performed for the award of ONE mark.

10 1717 1m

11 All numbers matched correctly as shown:

34

210

14

25

0.25

0.4

0.75

0.2

1m Do not award the mark if additional incorrect lines are drawn.

Lines need not touch the numbers provided the intention is clear.

12a

12b

4

Monday AND Thursday

1m

1m

Do not accept a list of days of the week.

Accept unambiguous abbreviations or recognisable misspellings.

Accept days written in either order.

13 Award TWO marks for numbers written in the correct regions as shown:

factors of 30

65 8

7

factors of 40

If the answer is incorrect, award ONEmark for any three numbers written in the correct regions.

Up to2m

Do not accept numbers written in more than one region.

Accept alternative indications such as lines drawn from the numbers to the appropriate regions of the diagram.

9



14a

14b

20001800

1945

computer

1810

tin can

1876

telephone

Answer for tin can joined to the time line in the range 1805 to 1815 exclusive.

Answer for computer joined to the time line in the range 1940 to 1950 exclusive.

1m

1m

Lines need not touch the time line provided the intended accuracy is clear.

15a

15b

Two numbers circled as shown:

71 72 73 74 75

An explanation which recognises that 1003 is not a multiple of 3, eg:

‘Because 1003 is not divisible by 3’

‘Because 1003 is not a multiple of 3’

‘Because 1003 is not in the 3 times table’

‘Because I divided 1003 by 3 and there was a remainder’

‘Because 1003 ÷ 3 has a decimal answer’

‘Because 1 + 0 + 0 + 3 = 4, and 4 is not a multiple of 3’

‘Because 1003 has a digital sum of 4’

‘Because 1002 is the nearest in the 3 times table’

‘Because 1000 is not divisible by 3’

‘Because 999 is divisible by 3’.

1m

1m

U1

Do not award the mark if additional incorrect numbers are circled.

Accept alternative unambiguous indications, eg ticks, crosses.

No mark is awarded for circling ‘No’ alone.

Do not accept vague or arbitrary explanations, eg:

‘Because 1003 ends in 3’

‘Because 1003 is in the third column’

‘Because if you keep going in 3s you will go past it’.

If ‘Yes’ is circled but a correct unambiguous explanation is given, then award the mark.

10



16 Award TWO marks for three shapes drawn correctly on the diagram as shown:

If the answer is incorrect, award ONEmark for:

the ‘L’ shape and any one of the two circles drawn correctly

OR

both circles drawn correctly AND the ‘L’ shape drawn in the correct square but orientated incorrectly.

Up to2m

Accept slight inaccuracies in drawing provided the intention is clear.

Circles need not be shaded.

17a

17b

6

An explanation which recognises that a total of 10 children read between 4 and 6 books, eg:

‘10 children altogether read between 4 and 6 books, and 7 + 1 makes 8, so that leaves 2 children’

‘Because 7 add 1 is 8, and you need 2 more’

‘Because 10 children read 4 to 6 books’

‘8 and 2 more make 10 children altogether’

‘1 + 7 = 8, 8 + 2 = 10’.

1m

1m

U1


‘Because 7 and 1 make 8’

‘Because there are 2 children left’.

18 196.45 1m


If the answer is incorrect, award ONEmark for evidence of appropriate working, eg

15 ÷ 3 = 5

5 × 10 = wrong answer

Up to2m

U1 Calculation must be performed for the award of ONE mark.

20a

20b

Answer in the range 110 to 3

20 inclusive.

Answer in the range 40 to 50 inclusive.

1m

1m

Range includes 17 , 1

8 , 19 and 1

10

Accept decimals (0.1 to 0.15 inclusive) or percentages (10% –15% inclusive).

11

Test A question 21

Markers will use a transparent overlay of this page to mark pupils’ answers to this question.

72°

7cm

10 cm


21 Award TWO marks for a triangle drawn with an angle in the range 70° to 74° inclusive AND length of sloping line in the range 6.9cm to 7.1cm inclusive (ie upper vertex of triangle within inner box on diagram).


a completed triangle drawn with an angle in the range 70° to 74° inclusive.

OR

a completed triangle drawn with an angle in the range 69° to 75° inclusive AND length of sloping line in the range 6.8cm to 7.2cm inclusive.

Up to2m

Accept drawings where any side has been extended past a vertex.

Accept drawings which do not use the given 10cm base line, provided they have used a line with a length in the range 9.9cm to 10.1cm inclusive.

Accept for ONE mark drawings not using the given 10cm base line which have a base line outside the range 9.9cm to 10.1cm, provided they have an angle in the range 70° to 74° inclusive AND a sloping line in the range 6.9cm to 7.1cm inclusive.

Accept for ONE mark drawings of incomplete triangles, provided they have an angle in the range 70° to 74° inclusive AND a sloping line in the range 6.9cm to 7.1cm inclusive.

12




If the answer is incorrect, award ONEmark for evidence of appropriate working which contains no more than ONE arithmetical error, eg:

long division algorithm wrong answer16 848

80048

–480

short division algorithm wrong answer

16 84 84

repeated addition / subtraction methods, eg

848–400 25 × 16 448–400 25 × 16

48–48 3 × 16

0 wrong answer

repeated halving, eg

848 ÷ 2 = 424

424 ÷ 2 = 212

212 ÷ 2 = 106

106 ÷ 2 = wrong answer

Up to2m

In all cases accept follow through ofONE error in working.

Calculation must be performed for the award of ONE mark.

Do not award any marks if the fi nal answer is missing.

Variations on algorithms are acceptable, provided they represent a viable and complete method.

Short division methods must be supported by evidence of appropriate carrying fi gures to indicate use of a division algorithm.

No mark is awarded for repeated addition / subtraction the wrong number of times.

No mark is awarded for repeated halving the wrong number of times.

23 Award TWO marks for all three numbers, as shown:

94, 95, 96


two numbers correct and none incorrect

OR

three numbers correct and one incorrect

OR

93, 94, 95, 96, 97

Up to2m

U1

Accept numbers written in any order.

All three numbers and no incorrect numbers must be given for the award of TWO marks.

13

Test B questions 1–6


1a

1b

4

599

1m

1m

2 Award TWO marks for the four lines drawn as shown:

greater than 100

less than 100

equal to 100

11 × 11

4 × 5 × 6

56 + 27 + 17

835 – 745

4000 ÷ 50

If the answer is incorrect, award ONEmark for three correct lines drawn AND not more than one incorrect line drawn.

Up to2m

Do not award any marks if two or more incorrect lines are drawn.

Lines need not touch the boxes provided the intention is clear.

3a

3b

5

2

1m

1m

49 1 + 9 1 + 1 9 = 201

OR

9 9 + 9 1 + 1 1 = 201

1m

U1

Accept the three two-digit numbers written in any order.

5 125 1m

6a

6b

£10.51

Award TWO marks for the correct answer of £2.26

If the answer is incorrect, award ONEmark for evidence of appropriate method, eg

34.99 + 12.75 = 47.74

50 – 47.74

OR

50 – 12.75 – 34.99

1m

Up to2m

Accept for ONE mark £226 OR £226p as evidence of appropriate method.

Answer need not be obtained for the award of ONE mark.

14



7a

7b

First column of table completed correctly.

Second column of table completed correctly.

1m

1m

Accept alternative unambiguous indications such as Y and N.

8a

8b

£14.40

20

1m

1m

Do not accept £14.4

Do not accept £20

9 (5, 2) 1m Coordinates must be written in the correct order.

Accept unambiguous answers written on the diagram.

10 Numbers circled as shown:

30 40 50 60 70

1m Accept alternative unambiguous indications, eg numbers ticked, crossed or underlined.

11 Answer in the range 65 to 75 inclusive. 1m

12 1 5 9 13 1m

15



13a

13b

Any odd numbered multiple of 10, ie 10 OR 30 OR 50 OR 70 OR 90 ORany number ending with any of the pairs of digits above.

An explanation which recognises that all multiples of 20 are also multiples of 10, eg:

‘Because all the numbers in the 20 times table are also in the 10 times table’

‘Because all multiples of 20 are multiples of 10’

‘Because 20 is in the 10 times table’

‘All multiples of 20 go in box A because 10 goes into them’

‘20 is a multiple of both 20 and 10, and so is 40, 60, etc’

‘Because if it’s not a multiple of 10, it can’t be a multiple of 20’

‘Because if it is a multiple of 20, it has to be a multiple of 10’

‘Because 10 is a factor of 20’.

1m

1m

U1


‘Because 40 is a multiple of 10’

‘Because they would be in box A instead’

‘Because all the multiples of 10 are multiples of 20’

‘Because 10 is a multiple of 20’.

14 £11.25 1m

15 Any rectangle with an area of 8 squares, eg

OR

1m Accept slight inaccuracies in drawing provided the intention is clear.

16



16 Award TWO marks for four facescorrectly shaded as shown:


only the correct four faces markedAND at least two shaded correctly

OR

four faces shaded correctly AND one shaded incorrectly

OR

three faces shaded correctly AND none shaded incorrectly.

Up to2m

U1

The width of each shaded rectangle is irrelevant provided the intention is clear.



800 – 500 = 300

300 ÷ 5

Up to2m

U1 Answer need not be obtained for the award of ONE mark.

18a

18b

Answer in the range 3:10pm to 3:20pm inclusive.

Answer in the range 13 degrees to14 degrees inclusive.

1m

1m

The answer is a specifi c time(see page 5 for guidance).



45 ÷ 3 = 15

15 × 2

Up to2m


17



20 Award TWO marks for all three numbers in order as shown:

129

AND

7492

AND

51

If the answer is incorrect, award ONEmark for two out of three numbers correct.

Up to2m

Do not accept 129.0 OR 7492.0 OR51.0 OR any other equivalent answers with zeroes after the decimal point.

21 40% 1m Do not accept equivalent fractions or decimals.

22a

22b

400

1200g OR 1.2kg

OR

for fi nding the correct difference between 1.6kg and the answer given for 22a.

1m

1m

Answer must be in grams.

Accept 1200 OR 1.2 OR 1kg 200g

23 Two numbers circled as shown:

29 39 49 59 69

1m Do not award the mark if additional incorrect numbers are circled.

Accept alternative unambiguous indications, eg numbers ticked, crossed or underlined.

24 Diagram completed as shown:

BA

1m Accept slight inaccuracies in drawing (see page 3 for guidance).



17.5 × 4 = 70

70 ÷ 5

Up to2m

U1 Accept for ONE mark 140 OR 1.4 as evidence of appropriate method.


18

Mark scheme for the mental mathematics test

Applying the mark scheme

Please note that pupils will not be penalised if they record any information given in

the question or show their working. Markers will ignore any annotation, even if in the

answer space, and mark only the answer. Markers will accept an unambiguous answer

written in the stimulus box, or elsewhere on the page.

Full mark scheme information is given on page 20. In addition, a ‘quick reference’

mark scheme is provided on page 19. This is presented in a similar format to the pupil’s

answer sheet.

General guidance

The general guidance for marking the written tests also applies to marking the mental

mathematics test. In addition, the following principles apply.

1. Unless stated otherwise in the mark scheme, accept answers written in words, or

a combination of words and fi gures.

2. Where units are specifi ed, they are given on the answer sheet. Pupils are not

penalised for writing in the units again.

3. Where answers are required to be ringed, do not accept if more than one answer is

ringed, unless it is clear which is the pupil’s intended answer. Accept also any other

way of indicating the correct answer, eg underlining.

Practice question

3 6

Time: 5 seconds

1 200

2 45 p

5 9900

4 3.4

17 0.7 0.077 0.707

0.77 7.007

Time: 15 seconds

16 60

18 32

19 £ 11.70

20 15 girls

15 0.009

10 5

11 1012

Accept 10.5 or equivalent fractions

12 –3 °C Do not accept 3–

13 48 cm2

14 110

Accept 0.1 or 10% or equivalent

fractions

7 450

Time: 10 seconds

6 710

8 35p

Mental mathematics 2006quick reference mark scheme

19

9 150 mmDo not accept

15cm

Mental mathematics questions 1–20


1 200 1m

2 45p 1m

3 6 1m

4 3.4 1m

5 9900 1m

6 710 1m

7 450 1m

8 35p 1m

9 150mm 1m Do not accept 15cm

10 5 1m

11 1012

1m Accept 10.5 OR equivalent fractions.

12 –3°C 1m Do not accept 3–

13 48cm2 1m

14 1m Accept 0.1 OR 10% OR equivalent fractions.

15 0.009 1m

16 60 1m

170.7 0.077 0.707

0.77 7.007

1m Accept any other way of indicating the answer, eg underlining.

Do not accept if more than one answer is indicated unless the pupil’s intention is clear.

18 32 1m

19 £11.70 1m

20 15 girls 1m

20

110

EARLY YEARS

NATIONALCURRICULUM5–16

GCSE

GNVQ

GCE A LEVEL

NVQ

OTHERVOCATIONALQUALIFICATIONS

For more information, contact:

QCA, 83 Piccadilly, London W1J 8QA

For more copies, contact:

QCA Orderline, PO Box 29, Norwich NR3 1GN

Tel: 08700 60 60 15 Fax: 08700 60 60 17

Email: [email protected]

Order ref: QCA/06/1900 (mark schemes pack) 270003

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